Right-hander Brad Peacock and catcher Max Stassi also went to Houston in Monday's deal.
Lowrie batted .244 with 16 homers and 42 RBI in 97 games with Houston. He missed two months with ankle and thumb injuries. The Astros got rid of his $2.4 million salary for this season and will likely have the lowest payroll in the majors in 2013.
Rodriguez went 2-10 with a 5.37 ERA in 71 relief appearances last year with 78 strikeouts in 701/3 innings.
Carter batted .239 with 16 homers and 39 RBI in 67 games with Oakland last year, platooning at first base with left-handed hitting Brandon Moss.
The Astros move from the National League to the American League this season, joining the Athletics in the AL West.
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